Which of these numbers is prime? ${29,\ 69,\ 75,\ 84,\ 93}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 29 are 1 and 29. The factors of 69 are 1, 3, 23, and 69. The factors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. The factors of 93 are 1, 3, 31, and 93. Thus, 29 is a prime number.